Algebra & Number Theory
- Algebra Number Theory
- Volume 12, Number 3 (2018), 723-750.
Algebraic de Rham theory for weakly holomorphic modular forms of level one
We establish an Eichler–Shimura isomorphism for weakly modular forms of level one. We do this by relating weakly modular forms with rational Fourier coefficients to the algebraic de Rham cohomology of the modular curve with twisted coefficients. This leads to formulae for the periods and quasiperiods of modular forms.
Algebra Number Theory, Volume 12, Number 3 (2018), 723-750.
Received: 3 August 2017
Revised: 22 December 2017
Accepted: 22 January 2018
First available in Project Euclid: 28 July 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11F11: Holomorphic modular forms of integral weight
Secondary: 11F23: Relations with algebraic geometry and topology 11F25: Hecke-Petersson operators, differential operators (one variable) 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
Brown, Francis; Hain, Richard. Algebraic de Rham theory for weakly holomorphic modular forms of level one. Algebra Number Theory 12 (2018), no. 3, 723--750. doi:10.2140/ant.2018.12.723. https://projecteuclid.org/euclid.ant/1532743369